Lets take a look at how a position control system would look with a stepper + timing belt system. This won't consider loads and size of motor.
Preview: It gets close. A servo-motor belt driven system could be a possibility. A higher-end stepper (double resolution with a good driver) may do it, but would need to be looked at very carefully.
Say top linear speed = 4.5 m/s , and around 0.3s acceleration and deceleration. Thus 1s motion travels approx 3m, which leaves a little bit to spare vs the 8ft requirement.
Lets say 50mm diameter belt drive gear =~ 150mm circumference, thus to get 4500mm/s, we will need 30 rev/sec = 1800 RPM. With a properly sized driver and modest load, you could get a standard 200step/rev stepper motor to 300RPM (1000 step/s), so a 1:6 gearing for increased speed becomes required based on that.
Standard stepper resolution is 1/200 rev at full-step, 1/400 rev at half-step, which becomes 1/67 rev at half-step resolution after the 6x gear ratio. Multiply by drive gear circumference = 150mm/67 = 2.25mm nominal linear resolution at half step. Not good enough, but not impossibly far away.
Discussion with an industrial automation sales person might get something useful.